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Abstract

We demonstrate a compressed sensing, photon counting lidar system based on the single-pixel camera. Our technique recovers both depth and intensity maps from a single under-sampled set of incoherent, linear projections of a scene of interest at ultra-low light levels around 0.5 picowatts. Only two-dimensional reconstructions are required to image a three-dimensional scene. We demonstrate intensity imaging and depth mapping at 256 × 256 pixel transverse resolution with acquisition times as short as 3 seconds. We also show novelty filtering, reconstructing only the difference between two instances of a scene. Finally, we acquire 32 × 32 pixel real-time video for three-dimensional object tracking at 14 frames-per-second.

D. Donoho and I. Johnstone, “Threshold selection for wavelet shrinkage of noisy data,” in Proceedings of the 16th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, (IEEE1994), 1A24–A25

Donoho, D.

D. Donoho and I. Johnstone, “Threshold selection for wavelet shrinkage of noisy data,” in Proceedings of the 16th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, (IEEE1994), 1A24–A25

Johnstone, I.

D. Donoho and I. Johnstone, “Threshold selection for wavelet shrinkage of noisy data,” in Proceedings of the 16th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, (IEEE1994), 1A24–A25

D. Donoho and I. Johnstone, “Threshold selection for wavelet shrinkage of noisy data,” in Proceedings of the 16th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, (IEEE1994), 1A24–A25

Figures (8)

Experimental Setup A 780 nm, 10 Mhz, 2 ns pulsed laser diode flood illuminates a scene containing targets at different depths. Returning pulses are imaged onto a DMD array with resolution up to 256 × 256 pixels. A polarizer prevents flares from specular reflection. Light reflecting off DMD “on” pixels is directed through a narrow-band filter to a single-photon sensitive PMT module that produces TTL pulses. Typical count rates are about 2 million photons per second. A TCSPC module time-correlates photon arrivals with the outgoing pulse train to determine a TOF for each detected photon. A series of psuedorandom, binary patterns consisting of randomly permuted, zero-shifted Hadamard patterns are placed on the DMD with per-pattern dwell times as short as 1/1440 sec. These implement an incoherent sensing matrix. For each pattern, the number of photon arrivals and their total TOF is recorded. Our protocol is then used to reconstruct the intensity image and the depth map.

Short Exposure Scene from Fig. 2 acquired with rapid acquisition times. The intensity and depth maps in (a) and (b) were acquired in 23 seconds while (c) and (d) were acquired in only 3 seconds. At these exposure times, the intensity map regularly contains less than one photon per significant pixel, so it is impossible to raster scan.

Depth Calibration Depth maps of a rectangular cardboard cutout (a) are acquired at n = 32 × 32 pixel resolution with a typical reconstruction given in (b). The cutouts to-target distance was increased in increments of 15.52 cm (c) and 2.54 cm (d). Depths can accurately recovered to less than 2.54 cm for this scene.

Novelty Filtering (a) and (b) give photographs of two instances of a scene, where the ‘R’ has changed positions (including depth). (c) and (d) show high quality, long 6.07 minute exposure depth map reconstructions for the full current scene and difference image respectively. (e) and (f) show corresponding short 37 second exposure depth map reconstructions. Negative values in the difference image indicate the object’s former location.

Movie Frames from a depth-map movie (
Media 1), of a three-dimensional pendulum consisting of a baseball suspended by a 170 cm rope swinging through a 25 degree solid angle. The transverse resolution is 32×32 pixels with a frame rate of 14 frames per second.